WASHINGTON — It could be that the urgency surrounding the debt-ceiling debate has simply hit its boiling point.

Or maybe it was because the president of the United States interrupted “The Bachelorette” with a dire announcement that if Washington politicians don’t stop fighting among themselves, the entire global economy could collapse.

Either way, after a set of prime-time speeches Monday — first by President Barack Obama and then by GOP House Speaker John Boehner — House websites were so overloaded with e-mails, some shut down. General “leave a comment” voice-mail boxes quickly filled. And on Tuesday morning, there was such a logjam of incoming calls from constituents, many Hill staffers retreated to hallways with cellphones so they could take calls.

“I was watching the speech, and when I heard the president say, ‘Call your congressman,’ I thought, ‘Oh, boy, here it comes,’ ” said Joe Megyesy, spokesman for Rep. Mike Coffman, a Republican from Aurora.

When Coffman’s Lone Tree office opened for business Tuesday, there were 90 voice mails, and the congressman received another 300 or so calls before noon, in addition to 1,400 e-mails.

“It’s a lot of passion and frustration,” said Megyesy, who will package the comments and deliver them to Coffman, who will likely remain in Washington until there is some kind of accord. “Some of them are saying, ‘Make a deal, compromise’; some are saying, ‘Stick to your guns.’ “

Colorado Democratic Sens. Mark Udall and Michael Bennet were receiving between 100 and 200 calls an hour — more than double what they normally get.

Rep. Diana DeGette, a Denver Democrat, said that in addition to all the calls to her office, she’s getting calls from personal friends, wondering “what the heck is going on.”

DeGette scribed an angry letter to Obama, Boehner and Senate Majority Leader Harry Reid on Tuesday, urging them to find a compromise.

“I’m sick of the gamesmanship,” she said. “Everyone’s just putting not just our economy, but the world’s economy, at risk.”

Obama, in his prime-time address, encouraged Americans to call members of Congress and urge a compromise.

“The American people may have voted for divided government, but they didn’t vote for a dysfunctional government,” he said. “So I’m asking you all to make your voice heard. If you want a balanced approach to reducing the deficit, let your member of Congress know. If you believe we can solve this problem through compromise, send that message.”

It was a tactic that has been used before by Franklin D. Roosevelt, when he was the governor of New York, said Gerard Hauser, professor of communication at the University of Colorado at Boulder.

“That’s a fairly consistent rhetorical strategy used by both parties, and it doesn’t serve us well because we don’t get focused on the nature of the problem,” Hauser said.

University of Virginia political scientist Larry Sabato was more cynical.

“I don’t think (all the phone calls) will make a bit of difference,” he said. “This is not the kind of dilemma that will be solved by a bunch of telephone calls.”

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